The rest of this web page will try to show you how to complete the square.

Now, you might be saying to yourself that $$ x^2 + 10x = 24 $$ could easily be solved without any fancy new methods (You could easily factor it, for instance.)
And, this of course is true. However, it turns out there are times when completing the square comes in very handy and will help you do a variety of things including convert the equations of circles, hyperbolas, ellipses into forms that make it much easier to work with these shapes.

If you haven't heard of these conic sections yet,don't worry about it. But, trust us, completing the square can come in very handy and can make your life much easier when you have to deal with certain types of equations.

Formula for Completing the Square

To best understand the formula and logic behind completing the square, look at each example below and you should see the pattern that occurs whenever you square a binomial to produce a perfect square trinomial.